Preheat the oven to 375°F and place the racks in the bottom third and top third positions. Prepare a 13x9 inch baking dish by spraying the bottom and sides with nonstick cooking spray.
For the shrimp, add butter to a large, nonstick pan and melt over medium heat. Add the shallots and ¼ teaspoon salt and cook until translucent, for 3-4 minutes. Add the garlic and cook for an additional 1 minute until fragrant. Add in the pieces of shrimp, Old Bay, and ½ teaspoon salt and cook for 1 minute, stirring. (You do not want to cook completely at this step, as they will continue to cook in the oven.)
Remove the shrimp from the heat and add to a medium bowl and stir in the crab.
For the ricotta filling, stir together the ricotta, drained spinach, lemon juice, zest, parsley, and ½ teaspoon salt.
For the bechamel, in the same pan used for the shrimp, set over medium heat and melt the butter. Once melted, sprinkle the flour over the butter and whisk until a paste forms and cook for about 2 minutes to cook out the raw flour taste. Slowly stir in the white wine, whisking vigorously, followed by the half and half. Stir in the clam juice, nutmeg, hot sauce, and 1 ½ teaspoons salt and let it come to a simmer, stirring occasionally. Do not boil. The sauce is ready when it has thickened and can coat the back of the spoon without being too runny. Remove from the heat and taste for seasoning and adjust to your taste.
For the shredded cheese mixture, combine all cheeses into a medium bowl and toss together.
To assemble, spoon ½ cup of the bechamel sauce into the prepared baking dish. Stir the shrimp mixture along with the parsley and tarragon into the remaining bechamel sauce. Top the bechamel with a layer of lasagna noodles. Spread one-third of the ricotta mixture over the noodles, followed by one-third of the shrimp-bechamel mixture, then sprinkle with one-third of the shredded cheese. Repeat with another layer of lasagna noodles, one-third of the ricotta mixture, one-third of the shrimp-bechamel mixture, and one-third of the shredded cheese. Finish with a final layer of lasagna noodles, the remaining ricotta mixture, the remaining shrimp-bechamel mixture, and the remaining shredded cheese, spreading it evenly over the top.
Cover with foil, place on a baking sheet, then place on the bottom third rack and bake for 40-45 minutes. Remove the foil, then move the pan to the top third rack and continue baking for an additional 10-15 minutes, until the top is bubbly and brown.
Remove from the oven, sprinkle with the remaining parsley, and let sit for 15 minutes. Then serve and enjoy immediately.